An example of a voltage-controlled oscillator having two control terminals will be described.
FIG. 1 is a circuit diagram showing a differential type VCO having two control terminals. The VCO has first control terminal 1, second control terminal 2, power supply terminal 3, output terminals 4a, 4b, constant current source 5, variable capacitive section 160, inductors 7a, 7b and cross-coupled transistors 8a, 8b. Inductors 7a, 7b and variable capacitive section 160 configure a resonator circuit. Here, a circuit structure of variable capacitive section 160 is not specifically shown.
As shown in FIG. 1, power supply terminal 3 to which the potential of VDD is applied is connected with constant current source 5. The output of the source is divided into two wirings. One of the two wirings is connected with inductor 7a, output terminal 4a and cross-coupled transistor 8a between constant current source 5 and a ground, sequentially. The other wiring is connected with inductor 7b, output terminal 4b and cross-coupled transistor 8b between constant current source 5 and a ground, sequentially.
Variable capacitive section 160 is connected between node A which is between inductor 7a and output terminal 4a of the one wiring, and node A′ which is between inductor 7b and output terminal 4b of the other wiring. Variable capacitive section 160 is provided with first control terminal 1 and second control terminal 2 for applying a voltage for capacitance control.
A gate terminal of cross-coupled transistor 8a is applied with potential to be outputted from output terminal 4b and a gate terminal of cross-coupled transistor 8b is applied with potential to be outputted from output terminal 4a. 
Capacitance Cv(vc1, vc2) of variable capacitive section 160 depends on both a voltage (vc1) of first control terminal 1 and a voltage (vc2) of second control terminal 2. For the differential type VCO, it is deemed that Cv(vc1, vc2) indicates a capacitance of only one side of the differential. As the voltage to be applied to first control terminal 1 and second control terminal 2 changes, the capacitance of variable capacitive section 160 also changes, so that the oscillation frequency is thus controlled. The oscillation frequency of the VCO is approximately expressed by equation (1) below.
                    [                  Equation          ⁢                                          ⁢          1                ]                                                                      f          ⁡                      (                                          v                                  c                  ⁢                                                                          ⁢                  1                                            ,                              v                                  c                  ⁢                                                                          ⁢                  2                                                      )                          =                              1                          2              ⁢              π                                ·                      1                                          L                ·                                  [                                                            C                      f                                        +                                                                  C                        v                                            ⁡                                              (                                                                              v                                                          c                              ⁢                                                                                                                          ⁢                              1                                                                                ,                                                      v                                                          c                              ⁢                                                                                                                          ⁢                              2                                                                                                      )                                                                              ]                                                                                        (        1        )            
wherein Cf indicates attributes of parts except variable capacitive section 160, such as cross-coupled transistors 8a, 8b and the like. For the differential type VCO, it is deemed that Cf indicates a capacitance of only one side of the differential. Although center voltages of the voltage (vc1) of first control terminal 1 and the voltage (vc2) of second control terminal 2 are not necessarily the same, it is here considered that both are the same, which is denoted as v0. At this time, a gain of the VCO (oscillation frequency sensitivity for vc1) can be expressed by equation (2) below.
                    [                  Equation          ⁢                                          ⁢          2                ]                                                                                  K            VCO                    ⁡                      (                                          v                                  c                  ⁢                                                                          ⁢                  1                                            =                              v                0                                      )                          =                                            -                              1                                  4                  ⁢                  π                  ⁢                                      L                                                                        ·                          1                                                [                                                            C                      f                                        +                                                                  C                        v                                            ⁡                                              (                                                                                                            v                                                              c                                ⁢                                                                                                                                  ⁢                                1                                                                                      =                                                          v                              0                                                                                ,                                                      v                                                          c                              ⁢                                                                                                                          ⁢                              2                                                                                                      )                                                                              ]                                                  3                  /                  2                                                      ·                                          ∂                                  C                  v                                                            ∂                                  v                                      c                    ⁢                                                                                  ⁢                    1                                                                                ⁢                      ❘                                          v                                  c                  ⁢                                                                          ⁢                  1                                            =                              v                0                                                                        (        2        )            
The VCO having the two control terminals as shown in FIG. 1 can be applied to a phase-locked loop (PLL) circuit or to a clock data recovery (CDR) circuit.
As examples of these, second control terminal 2 is drawn out as an external terminal of the circuit. By adjusting the voltage (vc2) to be applied to the external terminal, Cv(vc1, vc2) of equation (1) is thus changed, so that a control of a center frequency is performed. Here, the center frequency is defined as an oscillation frequency when the voltage of first control terminal 1 is the center voltage (v0). Thereby, the VCO is enabled to perform a multi-band operation, so that a multi-band operation of the PLL and a multi-bit operation of the CDR are resultantly possible. Further, it is possible to apply an architecture having the two control terminals in a loop to the PLL circuit.
In the following, a specific example of variable capacitive section 160 will be described.
FIG. 2 is a circuit diagram that specifically shows a structure of variable capacitive section 160 in the differential type VCO shown in FIG. 1. Variable capacitive section 160 in this example has first variable capacitive elements 9a, 9b and second variable capacitive elements 10a, 10b, as a variable capacitive element. First variable capacitive elements 9a, 9b and second variable capacitive elements 10a, 10b are variable capacitance diodes.
As shown in FIG. 2, anodes of first variable capacitive elements 9a, 9b are connected to each other and to first control terminal 1. Anodes of second variable capacitive elements 10a, 10b are connected to each other and to second control terminal 2. Cathodes of first variable capacitive elements 9a and second capacitive element 10a are connected to each other and to node A of the wiring between inductor 7a and output terminal 4a. Cathodes of first variable capacitive elements 9b and second capacitive element 10b are connected to each other and to node A′ of the wiring between inductor 7b and output terminal 4b. 
In this case, one-side capacitance Cv(vc1, vc2) of variable capacitive section 160 is expressed by equation (3) below when a capacitance value of first variable capacitive elements 9a, 9b is given as C1(vc1) and a capacitance value of second variable capacitive elements 10a, 10b is given as C2(vc2).[Equation 3]Cv(vc1,vc2)=C1(vc1)+C2(vc2)  (3)
Accordingly, the oscillation frequency given by equation (1) can be expressed by equation (4) below.
                              [                      Equation            ⁢                                                  ⁢            4                    ]                ⁢                                                                                                f          ⁡                      (                                          v                                  c                  ⁢                                                                          ⁢                  1                                            ,                              v                                  c                  ⁢                                                                          ⁢                  2                                                      )                          =                              1                          2              ⁢              π                                ·                      1                                          L                ·                                  [                                                            C                      f                                        +                                                                  C                        1                                            ⁡                                              (                                                  v                                                      c                            ⁢                                                                                                                  ⁢                            1                                                                          )                                                              +                                                                  C                        2                                            ⁡                                              (                                                  v                                                      c                            ⁢                                                                                                                  ⁢                            2                                                                          )                                                                              ]                                                                                        (        4        )            
The VCO gain given by equation (2) can be expressed by equation (5) below.
                    [                  Equation          ⁢                                          ⁢          5                ]                                                                                  K            VCO                    ⁡                      (                                          v                                  c                  ⁢                                                                          ⁢                  1                                            =                              v                0                                      )                          =                                            -                              1                                  4                  ⁢                  π                  ⁢                                      L                                                                        ·                          1                                                [                                                                                                                                          C                            f                                                    +                                                                                    C                              1                                                        ⁢                                                          (                                                                                                v                                                                      c                                    ⁢                                                                                                                                                  ⁢                                    1                                                                                                  =                                                                  v                                  0                                                                                            )                                                                                +                                                                                                                                                                                          C                            2                                                    ⁡                                                      (                                                          v                                                              c                                ⁢                                                                                                                                  ⁢                                2                                                                                      )                                                                                                                                ]                                                  3                  /                  2                                                      ·                                          ⅆ                                  C                  v                                                            ⅆ                                  v                                      c                    ⁢                                                                                  ⁢                    1                                                                                ⁢                      ❘                                          v                                  c                  ⁢                                                                          ⁢                  1                                            =                              v                0                                                                        (        5        )            
In the meantime, for a case where the same voltage is applied to the first and second control terminals, another example of the variable capacitive section is disclosed in Japanese Unexamined Patent Publication No. 2004-260301.